Resumen de Nagata Spaces and wN-spaces which are preserved by Quasi-Perfect Maps

Shin-ichi Nitta, Iwao Yoshioka

• G.Ying and C.Good (2001) described that Lutzer's example (1971) asserts that neither Nagata spaces nor wN-spaces are necessarily preserved under quasi-perfect maps. We introduce some classes of spaces which are contained in the class of wN-spaces and show that these classes are invariant under quasi-perfect maps or closed almost-open maps, but not preserved by closed map nor open finite-to-one maps. We also show that in the realm of paracompact spaces, these new classes coincide with the class of M-spaces in the sense of Morita, and study conditions for metrizability of these classes.